### Abstract

This chapter provides an introduction to vector quantization and lattice quantization. The development shows that lattice-based vector quantizers can perform arbitrarily close to the rate distortion bound as the number of dimensions becomes large and that it may be possible to avoid entropy coding of the quantizer output points with lattice quantizers. Fast quantization algorithms are known for many important vector quantizers. The development in this chapter includes mathematical detail to be able to implement lattice quantizers for many applications and to allow judicious tradeoffs among the various lattice-based vector quantizers to be made. A mastery of the material in this chapter is a necessary background for a fruitful investigation of the literature on vector quantization and lattice quantizers; however, this material is not sufficient to conduct research on many fundamental theoretical issues which remain unresolved in lattice quantization, such as finding the Voronoi regions of certain lattices, and more detailed examination of the references is required to pursue this goal.

Original language | English (US) |
---|---|

Pages (from-to) | 259-330 |

Number of pages | 72 |

Journal | Advances in Electronics and Electron Physics |

Volume | 72 |

Issue number | C |

DOIs | |

State | Published - Jan 1 1988 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Condensed Matter Physics
- Electrical and Electronic Engineering

### Cite this

*Advances in Electronics and Electron Physics*,

*72*(C), 259-330. https://doi.org/10.1016/S0065-2539(08)60560-0

**Lattice Quantization.** / Gibson, Jerry D.; Sayood, Khalid.

Research output: Contribution to journal › Article

*Advances in Electronics and Electron Physics*, vol. 72, no. C, pp. 259-330. https://doi.org/10.1016/S0065-2539(08)60560-0

}

TY - JOUR

T1 - Lattice Quantization

AU - Gibson, Jerry D.

AU - Sayood, Khalid

PY - 1988/1/1

Y1 - 1988/1/1

N2 - This chapter provides an introduction to vector quantization and lattice quantization. The development shows that lattice-based vector quantizers can perform arbitrarily close to the rate distortion bound as the number of dimensions becomes large and that it may be possible to avoid entropy coding of the quantizer output points with lattice quantizers. Fast quantization algorithms are known for many important vector quantizers. The development in this chapter includes mathematical detail to be able to implement lattice quantizers for many applications and to allow judicious tradeoffs among the various lattice-based vector quantizers to be made. A mastery of the material in this chapter is a necessary background for a fruitful investigation of the literature on vector quantization and lattice quantizers; however, this material is not sufficient to conduct research on many fundamental theoretical issues which remain unresolved in lattice quantization, such as finding the Voronoi regions of certain lattices, and more detailed examination of the references is required to pursue this goal.

AB - This chapter provides an introduction to vector quantization and lattice quantization. The development shows that lattice-based vector quantizers can perform arbitrarily close to the rate distortion bound as the number of dimensions becomes large and that it may be possible to avoid entropy coding of the quantizer output points with lattice quantizers. Fast quantization algorithms are known for many important vector quantizers. The development in this chapter includes mathematical detail to be able to implement lattice quantizers for many applications and to allow judicious tradeoffs among the various lattice-based vector quantizers to be made. A mastery of the material in this chapter is a necessary background for a fruitful investigation of the literature on vector quantization and lattice quantizers; however, this material is not sufficient to conduct research on many fundamental theoretical issues which remain unresolved in lattice quantization, such as finding the Voronoi regions of certain lattices, and more detailed examination of the references is required to pursue this goal.

UR - http://www.scopus.com/inward/record.url?scp=77957014005&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957014005&partnerID=8YFLogxK

U2 - 10.1016/S0065-2539(08)60560-0

DO - 10.1016/S0065-2539(08)60560-0

M3 - Article

AN - SCOPUS:77957014005

VL - 72

SP - 259

EP - 330

JO - Advances in Imaging and Electron Physics

JF - Advances in Imaging and Electron Physics

SN - 1076-5670

IS - C

ER -